Question

If (2 - 4i) is a solution to a polynomial equation, is the complex conjugate, 2 + 4i, also a solution?

Answer 1

If the polynomial has Real number coefficients, then the complex conjugate of an imaginary root is also a root.

Explanation:

So, if the coefficients are real numbers, then the answer is "yes.

If the coefficients are not known to be real, then the answer is "maybe yes, maybe no".
`x-(2-4i)=0` has only one zero, namely `2-4i`

`(x-(2-4i))(x-i)=0` has two solutions, `2-4i` and `i`.